Momentum scale dependence of the net quark number fluctuations near chiral crossover

We investigate properties of the net baryon number fluctuations near chiral crossover in a hot and dense medium of strongly interacting quarks. The chirally invariant quark-antiquark interactions are modeled by an effective quark-meson Lagrangian. To preserve remnants of criticality in the O(4) universality class, we apply the functional renormalization group method to describe thermodynamics near chiral crossover. Our studies are focused on the influence of the momentum cuts on the critical behavior of different cumulants of the net quark number fluctuations. We use the momentum scale dependence of the flow equation to examine how the suppression of the momentum modes in the infrared and ultraviolet regime modifies generic properties of fluctuations expected in the O(4) universality class. We show, that the pion mass $m_\pi$ is a natural soft momentum scale at which cumulants are saturated at their critical values, whereas for scales larger than $2m_\pi$ the characteristic O(4) structure of the higher order cumulants get lost. These results indicate, that when measuring fluctuations of the net baryon number in heavy ion collisions to search for a partial restoration of chiral symmetry or critical point, a special care have to be made when introducing kinematical cuts on the fluctuation measurements.